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Question Number 71894 by 20190927 last updated on 21/Oct/19

$$\underset{x\to \frac{\pi }{2}}{\lim }{\left(\sin \mathrm{x}\right)}^{\mathrm{tanx}}$$

Commented by kaivan.ahmadi last updated on 21/Oct/19

$$=e^{{lim}_{x\to \frac{\pi }{2}}(sinx-1)tanx}=e^{{lim}_{x\to \frac{\pi }{2}}\frac{sinx-1}{cotx}}=$$$$e^{{lim}_{x\to \frac{\pi }{2}}\frac{cosx}{-(1+{cot}^{2}x)}}=e^0=1$$

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